Orthogonal Frequency Division Multiplexing (OFDM), also referred to as “multi-carrier modulation” (MCM) or “discrete multi-tone modulation” (DMTM), splits up and encodes high-speed incoming serial data, modulating it over a plurality of different carrier frequencies (subcarriers) within a communications channel to transmit the data from one user to another. The high-speed serial information is broken up into a plurality of lower-speed sub-signals that are transmitted simultaneously over the subcarriers in parallel.
Assuming that each subcarrier is a sinusoid, the effect of modulation on the spectrum of the modulated carrier is to expand it outward from a spectral line to a sinc function, centered on the subcarrier frequency and having zero power points (“zeroes”) occurring at integer multiples of the modulation frequency (bit rate). A sinc function has the general form:
      sin    ⁢                  ⁢          c      ⁡              (        x        )              =            sin      ⁡              (        x        )              x  
In the specific case of a subcarrier ωS being modulated at a bit rate ωM, the frequency spectrum F(ω) is given by:
      F    ⁡          (      ω      )        =            sin      ⁢                          ⁢              c        ⁡                  (                                    ω              M                        ⁡                          (                              ω                -                                  ω                  S                                            )                                )                      =                  sin        ⁡                  (                                    ω              M                        ⁡                          (                              ω                -                                  ω                  S                                            )                                )                                      ω          M                ⁡                  (                      ω            -                          ω              S                                )                    
which has a peak at ωS and zeroes at integer multiples of ωM, both above and below ωS.
By spacing the subcarrier frequencies at intervals of the symbol frequency (bit rate), the peak power component of each modulated subcarrier lines up exactly with zero power components of the other modulated subcarriers, thereby providing orthogonality (independence and separability) of the individual subcarriers. This scheme can be applied to a large number of subcarriers spaced at the symbol frequency (bit rate), yielding good spectral efficiency with minimal interference between the subcarriers (inter-channel interference, or ICI).
An exemplary channel spacing for an OFDM communication system is illustrated in FIG. 1, which is a graph 100 illustrating spectral power (vertical axis, arbitrary units) versus frequency (horizontal axis, arbitrary units), showing the spectra of three modulated subcarriers 102, 104 and 106. In the example of FIG. 1, the subcarriers 102, 104 and 106 are modulated at a bit rate equivalent to 300 frequency “units”, as indicated on the horizontal axis of the graph. The first subcarrier 102 has a center frequency of 100 “units” relative to a reference “zero frequency”, and has zero power points (zeroes) occurring at 400, 700 and 1000 frequency units. The second subcarrier 104 has a center frequency of 400 frequency units relative to the reference zero frequency, and has zeroes occurring at 100, 700 and 1000 frequency units. The third subcarrier 106 has a center frequency of 700 frequency units relative to the reference zero frequency, and has zeroes occurring at 100, 400 and 1000 frequency units. Each subcarrier's peak occurs at its center frequency, which aligns only with zero power points of the other subcarriers.
Due to the consistent channel spacing, subcarriers can be referred to by subcarrier number “i”, where “i” is an integer which can be positive, negative, or zero. Accordingly, the “ith” subcarrier SCi(t) can be expressed as follows:SCi(t)=cos [(ωc+iωs)t]
where:                ωc is the overall carrier reference frequency for the OFDM channel        ωs is the OFDM channel spacing frequency        
FIG. 2 is a block diagram illustrative of portion of an exemplary OFDM transmission system 200. In the OFDM transmission system 200 of FIG. 2, a high-speed input data stream 202 is presented at an input of a Serial-to-Parallel conversion block 204, which breaks up and encodes the high-speed data input stream 202 into a number of lower-speed data streams 206a, 206b, 206c, and 206d. Each lower-speed data stream 206a, 206b, 206c, and 206d modulates a respective subcarrier 208a, 208b, 208c, and 208d, to produce a respective modulated subcarrier 210a, 210b, 210c and 210d. The modulation rate (ωM) and subcarrier spacing (ωs) is chosen so that the modulated subcarriers 210a, 210b, 210c and 210d are orthogonal, as shown and described hereinabove with respect to FIG. 1. The modulated subcarriers 210a, 210b, 210c and 210d are then combined in a combining block 212 (shown as a summing element) to produce a composite OFDM output signal 214.
This technique of transmitting data simultaneously over multiple, orthogonal subcarriers permits OFDM-based wireless LANs (WLANs) and other OFDM-based communications networks to operate at higher aggregate data rates than is possible using other schemes with similar receiver complexity. For example, the OFDM-based wireless LAN standard specified by the Institute of Electrical and Electronic Engineers (IEEE Std 802.11a-1999—Supp. to IEEE Std 802.11-1999—“High-speed Physical Layer in the 5 GHz Band”; hereinafter “IEEE 802.11a”) can operate at data rates of up to 54 Mbps, approximately double the rate achievable using direct-sequencing techniques. In addition, RF signals that interfere with an OFDM signal will only destroy the portion of the OFDM transmitted signal related to the frequency of the interfering signal. Through the use of error-correcting codes (ECC), the damage associated with the destroyed portion of the OFDM transmitted signal can often be reconstructed.
An inherent advantage of OFDM is its low multi-path distortion (delay spread), resulting from the fact that high-speed data is sent in parallel over a plurality of subcarriers at relatively low data rates. Because of the lower data rate transmissions, individual symbol (bit) times are longer and differential signal delays due to multi-path reception are not nearly as significant as they would be in a single-channel system utilizing a higher data rate, wherein the symbol times would be shorter.
Many wired and wireless standards bodies have adopted OFDM for a variety of applications. For example, OFDM is the basis for the global standard for asymmetric digital subscriber line (ADSL) and for digital audio broadcasting (DAB) in Europe. In wireless networking applications, OFDM forms the basis of IEEE 802.11a and HiperLAN/2, which implement OFDM similarly. Their main differences lie in their available rates and preambles.
The IEEE 802.11a standard specifies an OFDM physical layer (PHY) that splits an information signal across 52 separate subcarriers to provide transmission of data at a rate of 6, 9, 12, 18, 24, 36, 48, or 54 Mbps. The 6-, 12-, and 24-Mbps data rates are mandatory for all IEEE 802.11a compliant systems. Four of the subcarriers are pilot tones (reference tones modulated with a known, repeating data sequence) that OFDM systems use as a reference to disregard frequency or phase shifts of the signal during transmission. A predetermined pseudo-random binary sequence is transmitted over the pilot subcarriers to prevent the generation of spectral lines. The remaining 48 subcarriers provide separate wireless pathways for sending the information in a parallel manner. The resulting subcarrier frequency spacing is 0.3125 MHz (for a 20 MHz channel with 64 possible sub-carrier frequency slots).